How Do You Calculate the Probability of a Heart Attack in a High-Risk Group?

[Calculator14]

Homework Statement

In a certain high-risk group, the chance of a person having suffered a heart attack is 70%. If four persons are chosen from the group, find the probability that at least one will have had a heart attack.

Homework Equations

(work shown below) these would be dependent

The Attempt at a Solution

(.7)/(4) = 2.8

 

[daveb]

It might be easier to think of the chance that a specific individual doesn't have a heart attack, so what are the chances that none of the individuals have heart attacks (and you might want to rethink the dependence).

 

[the_amateur]

your answer is wrong
i don think it is a dependent event

the probability of a person with heart attack is 0.7

so the probability that among 4 at least 1 has heart attack = 1 - probability that none have

= 1 - (0.3)$^{4}$
must be correct but verify it

 

[Laiva-59]

Amateur's answer is correct.

Your attempt doesn't make any sense.
Remember: probability can never be more than 1.

So if you find 2.8, think again.

 

[DeeNos]

I would like to clarify that the probability of a person having suffered a heart attack is not 70%, but rather the chance of a person in the high-risk group having suffered a heart attack is 70%. This is an important distinction to make when discussing probabilities.

To find the probability that at least one person will have had a heart attack in a group of four, we can use the complement rule. This states that the probability of an event not occurring is equal to 1 minus the probability of the event occurring. In this case, the event we are interested in is at least one person having had a heart attack, so the complement would be none of the four people having had a heart attack.

The probability of none of the four people having had a heart attack can be calculated by multiplying the probability of each person not having had a heart attack, which would be (1-0.7) = 0.3.

Therefore, the probability of at least one person having had a heart attack is 1 - 0.3^4 = 0.973 or 97.3%. This means that there is a high likelihood that at least one person in the group of four has had a heart attack.

Additionally, as a scientist, I would like to point out that this calculation is based on the assumption that the four people chosen from the high-risk group are independent events. If there are any factors that could make them dependent, such as shared genetics or lifestyle, the probability may be different. It is important to consider all relevant factors when making statistical calculations.